Calculus homework help

Calculus homework help. 1) F ind the deri vati ves of the fol lowing functions :
a) y = ln 2
3×9 b) y = 3
e
3x
2) Let f(x) = ln (x)
x
a) F ind the deri vati ve, f’ (x) .
b) Sol ve f’ (x) = 0
F ind the i ndefi nite integral.
3) a x2 x3 + 3 dx
4)
a
F ind the i ndefi nite integral :
x2
x – 1
dx
5)
a
Use substitution to find the in definite integral :
dx
2x ln x
6)
a
F ind th e indefin ite integral by substitution:
ln (5x)
x
d x
7)
a
Evaluate using su bstitution :
2
1
( x – 1 ) 2 – x dx
8)
a
E val uate, gi ve the exact value :
1
e x
1 + e x
d x
9) F ind the area of the shaded region:
10) T he demand f unction for a certai n product is gi ven by
p = – 0.01 x2 – 0.2 x + 12
where p represents the unit price in dol lars an d x is the quantity
demanded measured in units of a thousand.
D etermine the consumer surplus if the price is set at $ 4 .

Calculus homework help